My Automathography.

Thirty years at UWA.

After two delightful years at Missoula, in 1970 Beth and I packed up
and set out for the University of Western Australia, accompanied by
Jonathan aged 3 and Rosalie, 6 months. In 1970, the staff here numbered
about 15, and I was the first of a large influx which saw the size of
the Department double in 10 years. The old hands included Phil
Silberstein, Malcolm Hood, John Mahoney, Beryl Hume, Dave Hurley, Peter
Chapman, Ray Storer, Frank Gamblen, Des Fearnley-Sander, Ron List,
Frank Yeomans, Peter Wynter and Neville Fowkes, as well of course as
Larry Blakers, who had been the sole Head since the death of
Weatherburn. Tsoi Ma, Mike Fisher and Bob Sullivan started in the same
year as me and Rick McFeat shortly thereafter.

In those days the structure and content of the
first two years of mathematics courses was similar to what it is today,
although the names of the courses have changed. Hence it is not
misleading to call them low and high Calculus I and II, Linear Algebra
I and II and Probability and Statistics I and II. At different times I
have taught all of these courses except high Probability and
Statistics, and made some horrendous errors. One that sticks in my mind
is trying to prove the properties of the Wronskian in high Calculus I,
instead of just stating them. Even worse occurred one year when I
thought it would be helpful in low Calculus I to put all the lectures
onto transparencies. I must have believed that the students could copy
all this out and at the same time listen to me explaining it. My
student evaluations that semester are an all-time record low.

Upper undergraduate students in Mathematics
present a different set of problems. I feel privileged to have been in
contact with some fine young minds, who have gone on to spectacular
success in Universities and private life around the world. Some people
complain, as Socrates probably did, about falling standards. I have
found that as far as the upper échelon of mathematics students are
concerned, their motivation and preparation equals or surpasses those I
have encountered in the past.

Incidentally, during several study leaves I have
taught essentially the same material at the same level at UWA, Hawaii,
New Mexico, and Germany. I have found no real difference in average
quality of students or exam performance. The students even dressed the
same!

Right from the beginning of my sojourn in WA I
have been involved in enrichment of gifted and talented high school
students. For several years I ran a mentor programme aimed at
attracting Year 10 girls into mathematics, one of the success stories
being Jane Perkins. When Australia first entered the International
Mathematical Olympiad in the early 1980s I became the WA Director of
Olympiad Training, and have been privileged to introduce to
mathematical problem solving some exceptional high school students,
including Andrew Kepert, Andrew Hassell, Jeremy Liew, Kin Yan Chung,
Chris Barber, Akshay Venkatesh and Peter McNamara.

Along similar lines, for several years I ran a
'Problem of the Week' Competition for undergraduates at UWA, and when
that faded away, organised the Blakers Mathematics Competition
for Year 1 to 3 Undergraduates in all Western Australian Universities.
This started in 1997 and continues to attract entries from talented
students throughout WA.

Let me deal now with Research. I managed to extract two publications [1] and [2] from my PhD thesis. (The numbers refer to the List of Publications).
Then followed a lean three years during which I seemed to be getting
nowhere. During these years, I suggested to Larry Blakers the idea
which eventually led to the Research Report series. Then two events
occurred which gave my research a new lease of life. Firstly, the
arrival of the very active Cheryl Praeger sparked my interest in group
actions on graphs and their connection with abelian group
presentations. This led to my paper [14] and , in collaboration with
her and others, [17] and [22].

Secondly, we acquired a talented post-doctoral
fellow named Rod Bowshell who found some wonderful new ideas in my
earlier papers that I had not noticed myself! We wrote a joint paper
for Math. Annalen [6] which inaugurated the concept of E-ring, an idea
whose time had come. Over twenty papers in the area appeared over the
next few years, and fortunately for my ego, they all cited
Bowshell-Schultz. After this, the notion became too well-known, and is
now used without any citation, a sign I suppose of real success.

Incidentally, a similar thing happened in the
1990s. In 1988, I wrote a Research Report on self-splitting abelian
groups, that is, groups G for which every extension of G by G splits.
(The definition makes sense in the non-abelian group context--but is it
interesting?). Because the Report contained no definitive theorems, I
did not submit it for publication. It did however contain four unsolved
problems in the borderline area among abelian groups, category theory
and logic. Somehow, these problems captured the imagination of some
first-rate mathematicians, including Shelah, and at least ten papers
were published solving and extending my problems. This led to a steady
demand for the Research Report which was typed in a nasty format in the
days before TeX or even word-processors in the Department. In
self-defence, I submitted the original 1988 paper in 2000 to the
Bulletin of the Aust. Math. Soc. and it appeared in 2001, [44].

Returning now to the annus mirabilis 1977,
the Bowshell-Schultz paper
lead to a number of invitations to meetings and visits, and I have
probably averaged one international conference each 18 months since
then. Such Conferences, usually held in a salubrious part of the world,
have enabled Beth and me to visit some amazing places, including
Oberwolfach, Dublin, Wuerzburg, Honolulu, Padova, Venice, Crete,
Mexico, Las Cruces, New York, Houston, Seattle and the major cities of
Australia. Unfortunately, Rod Bowshell, to whom I owe so much, retired
from professional mathematics after his post-doc and opened a bookshop
in Sydney. He has continued his mathematical studies on an amateur
basis, but as far as I know, has not published his work.

Since 1977, I have averaged one major paper per
year. My areas of research have mainly been abelian p-groups and their
endomorphism rings and automorphism groups, torsion-free abelian groups
in general and almost completely decomposable groups in particular, and
general module theory which most occupies my mind at the moment. I have
also published minor papers in the areas of history of mathematics,
graph theory, elementary geometry and calculus for mathematics
teachers, book reviews and (believe it or not) Library Science, [11].
Apart from editing three Conference Proceedings, I have up to now 30
sole author papers and 25 joint publications, with collaborators from
Australia, USA, Germany, Mexico, Russia, Romania and Bulgaria. Thanks
to Nick Wormald, I have Erdos Number two.

I have organised three International Conferences
here in Perth, one on Algebraic Structures and Applications in 1980,
which was organised around an extended visit of Laszlo Fuchs, one on
Abelian Group Theory in 1987, and one on Abelian Groups, Rings and
Modules in 2000. In each case, we managed to attract over 40 overseas
visitors, and the Proceedings were published by Marcel Dekker [12], or
the American Mathematical Society, [24] and [42].

In 2000, I retired from paid employment but have
continued to teach and do research. My main interests continue to be in
Algebra, particularly modules and their endomorphism rings.